EML6223 Spring 2017

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Department of Mechanical and Materials Engineering

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This is the EML 6223 Vibration Analysis Course Spring 2017

Here is the EML6223 Syllabus

READ Chapter 1 and Chapter 2 as part of the review. Do problems out of chapter1: 4, 7, 9, 10, 11, 16, 22, 50, 51, 55, 56, 88, 89. Turn in problems 1.7, 1.9, 1.22, 1.50, 1.56, 1.89 next Tuesday, January 17

Here are problems 1-4, 1-7 and like 1-9, 1-10 and like 1-11

Here are problems like 1-17, 1-23a and 1-23b,

Here are problems 1-48, 1-49, 1-55 and like 1-56

Here are problems 1-91, 1-85, and 1-88

This material and all the linked materials provided, except where stated specifically, are copyrighted © Cesar Levy 2015 and is provided to the students of this course only. Use by any other individual without written consent of the author is forbidden.

READ Chapter 1 and Sections 2.1-2.5

Even though I have given you access to the solutions, you need to try to do the problems first so that you will know where you get stuck and then use the solutions to see you get past the problem. Just looking at the solutions does not help you understand the methodology in relation to the way you think about solving the problem. Just as with Dynamics, the only way to learn vibrations is to do as many problems as you can.

Here are problems 2-4, 2-6 and 2-7 Note that more comments about 2-7

Are found on the top of the page for problem 2-13

Here are problems 2-13 , 2-15. Note that the problem here is LIKE 2-13 in your book

But is not problem 2-13

Here are problems 2-17, 2-18, 2-19

Here are problems 2-26, 2-38

Here is the rest of 2-38, and problems 2-68, 2-79

Here is the rest of 2-79

Here is problem 2-69

Here is problem 2-33, problem 2-45, and problem 2-71

From here we begin Problems in free vibration with damping….

READ Chapter 2.6-2.8

Here are problems 2.88 and 2.90

Here are problems 2.84, 2.92 and 2.95

Here are problems 2.93, 2.96 and the rest of 2.90

Here are problems 2.106, and 2.122

Here are problems 2.112, 2.113 and 2.115 part a

Here is the rest of 2.115 and 2.116 and the rest of 2.116

Here is problem 2.145

Please start looking at the following problems

Here are problems 3.1, 3.2, 3.8, 3.10

Do problems 3.18, 3.19,3.25, 3.26—No solutions will be given for these…solutions to 3.19 and 3.25 are given in the back of your book.

Here are problems 3.29 and 3.33part1, 3.33part2 and 3.32

Other problems of Chapter 3 to be covered related to rotating unbalance and forced vibration.

Here are problems 3.54, 3.58

Here are problems 3.34 and 3.51 and 3.53

Here are problems 3.48 and 3.59

These problems deal with force transmitted and with vibration measuring equipment.

Here are problems 9.27, 9.32 and 9.34

Here is the rest of 9.34pt2 and 9.35

Here are problems 10.11, 10.12, 10.15

Please start reading the topics related to continuous systems, namely the vibrations of strings, beams, membranes and plates starting in chapter 8.

We spoke about two degree of freedom (2DOF) systems relating to masses and springs; and relating to linear and rotational displacements (Chapter 5 of our book). We found the natural frequencies and eigenfunctions for such systems. We spoke about the vibration absorber case and also the semi-definite case (case where the lowest natural frequency is = 0).

Here are problems 5.1, 5.4, 5.5, 5.20, 5.21, 5.34

We looked at the forced vibration of 2DOF systems (Chapter 5 of our book). We showed how the 2DOF system moves the natural frequencies away from the original forcing frequency and how we can tune the system so that the main mass can stop oscillating.

We started speaking about the vibration of continuous systems (Chapter 8), such as strings and longitudinal vibration of bars with and without end masses, deriving the governing equation for these cases, defining the boundary conditions and how one can obtain the solutions using the method of separation of variables. We showed how the boundary conditions may be used to obtain the frequencies and the eigenfunctions.

We completed the work on bars with end masses and showed graphically how one can find the natural frequencies for different cases when mbar/mend is less than, equal to and greater than 1. We derived and showed the similarity of torsional vibrations of bars. We also derived the governing equation of the Bernoulli-Euler beam, spoke about the boundary conditions and the assumptions made in the derivation of the equation.

We looked at the inclusion of an axial force leading to the dynamic buckling problem and discussed the variation of the frequency of vibration as a function of the ratio of the axial force to the Euler buckling load. We also looked at the Timoshenko beam theory in which the rotatory inertia and shear effects were included. Lastly, we starting the derivation of the 2-D membrane vibration equation which will be completed on Tuesday June 23.